Theorems · Theorem · order theory
le_sSup_of_le
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s : Set α} {a b : α}, b ∈ s → a ≤ b → a ≤ sSup s- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- le_transproof · cited by 985
- SupSet.sSupstatement · cited by 954
- le_sSupproof · cited by 79
- CompleteSemilatticeSupstatement and proof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- CompleteLattice.IsCompactElement.exists_finset_of_le_iSupproof · cited by 2
- continuous_sSup_rngproof · cited by 1